Worked example: using recursive formula for arithmetic sequence Our mission is to provide a free, world-class education to anyone, anywhere. Khan Academy is a 501(c)(3) nonprofit organization.From what I gather, I can use the alternating series test to check if an alternating series converges or diverges. Let's say, for example I have the series of $(-1)^k\\sin (\\frac{1}{k})$. I've prove...Question 7 1 / 1 pts Fiona has proved that a function, f (x), is an arithmetic sequence. How did she prove that? (1 point) She showed that an explicit formula could be created. She showed that a recursive formula could be created. She showed that f (n) ÷ f (n − 1) was a constant ratio.A recursive formula allows us to find any term of an arithmetic sequence using a function of the preceding term. Each term is the sum of the previous term and the common difference. For example, if the common difference is 5, then each term is the previous term plus 5. As with any recursive formula, the first term must be given.a. Write an explicit formula for the arithmetic sequence 4, 7, 10, 13, … . b. Compute the 30th term of the sequence. Mental Math Tell whether the graph of the function is a line, a parabola, a hyperbola, or none of these. a. f(x) = 6x2 b. =g(x) -2x c. h(x) = - __3 x2 d. j(x) = __17 x = 2 = = Vocabulary linear sequence, arithmetic sequence
How to prove absolute convergence by using the alternating
Question: Rishi Maharan's charge account statement shows an unpaid balance of $6,752.22. The monthly finance charge is 1.85% of the unpaid balance. After the finance charge was applied, Rishi has made new purchases of $150.75. What is the new account balance? $7,027.89 $7,030.67 $6,902.97 $6,877.14The arithmetic sequence is 8, 16, 24, 32, 40, 48, 56, «. Find the common difference. 16 ± 8 = 8 The sequence is increasing, so the common difference is positive: 8. Write the equation for the nth term of an arithmetic sequence with first term 8 and common difference 8. So, the function for this arithmetic sequence is f(n) = 8n. b.Question 7 1 / 1 pts Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? (1 point) She showed that an explicit formula could be created. She showed that a recursive formula could be created. She showed that f(n) ÷ f(n − 1) was a co nstant ratio. She showed that f(n) − f(n − 1) was a constant difference.The class of bounded arithmetic predicates (BA) is the smallest class containing the polynomial predicates and closed under bounded quantification ((∃w) ⩽y R(x, y, w) or (∀w) ⩽v R(x, y, w)).The bounded arithmetic predicates are a small subset of the recursively enumerable, but they include most of the standard examples from recursive function theory and form a basis for the r.e. sets
Zachs method is linear because the number of minutes
In the previous table, a n is called the general (or nth term) of the sequence. It is the rule by which all of the terms of the sequence can be generated. a 3 indicates the 3rd term of the sequence and a n+1 stands for the term right after a n. a n and a n+1 are called consecutive terms of a sequence.. Two of the types of sequences that are covered in your text are arithmetic and geometric.1) In particular, the exponents m , n , k need not be equal, whereas Fermat's last theorem considers the case m = n = k . The Beal conjecture , also known as the Mauldin conjecture and the Tijdeman-Zagier conjecture, states that there are no solutions to the generalized Fermat equation in positive integers a , b , c , m , n , k with a , b , and c being pairwise coprime and all of m , n , kSection 4.6 Arithmetic Sequences 203 You can rewrite the equation for an arithmetic sequence with fi rst term a 1 and common difference d in function notation by replacing a n with f(n). f(n) = a 1 + (n − 1)d The domain of the function is the set of positive integers.Jake has proved that a function, f(x), is a geometric sequence. How did he prove that?. A) He showed that an explicit formula could be created. B) He showed that a recursive formula could be created. C) He showed that f(n) ÷ f(n - 1) was a constant ratio. D) He showed that f(n) - f(n - 1) was a constant difference.The course-of-values for the function \(x^2\) records, among other things, that the number 4 is the value when the number 2 is the argument, that 9 is the value when 3 is the argument, etc. When a function \(f\) is a concept, Frege called the course-of-values for that concept its extension. The extension of a concept is something like the set
Well,
He showed that f(n) ÷ f(n - 1) used to be a consistent ratio.
f(n+1) / f(n) = r = constant RATIO
hope it' ll lend a hand !!
PS: nonetheless:
1. any person is not sufficient : if Jake proved THE expicit system is : f(n) = f0 * r^n then f(n) is geometric : so it depends upon WHAT explicit formula... it must be THIS ONE !!
2. similar for "a recursive formula could be created" : it will have to be : f(n+1) / f(n) = r = consistent RATIO
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